Answer:
The initial speed of the ball is 98.22 ft/s
The maximum height of the ball is 75.02 ft.
Step-by-step explanation:
Hi there!
Step-by-step explanation:
The position and velocity vectors of the ball can be calcualted as follows:
r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)
v = (v0 · cos α , v0 · sin α + g · t)
Where:
r = position vector at time t.
x0 = initial horizontal position.
v0 = initial velocity.
t = time.
α = launching angle.
y0 = initial vertical position.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
v = velocity vector at time t.
Let´s call r final to the position vector when the ball is caught (see attached figure). The components of r final are:
x = 300 feet
y = 0
Then, r final = (300 feet, 0)
Notice that the origin of the frame of reference is located at the launching point.
Then, when the ball is caught:
300 feet = x0 + v0 · t · cos α
0 = y0 + v0 · t · sin α + 1/2 · g · t²
We have a system of two equations with two unknowns (t and v0), so, let´s solve it.
Let´s solve the first eqation for v0:
300 feet = x0 + v0 · t · cos α
Since the frame of reference is located at the launching point (x0 = 0). Then:
300 feet = v0 · t · cos 45°
300 feet /( t · cos 45°) = v0
Now, let´s replace v0 in the secod equation of the system:
0 = y0 + v0 · t · sin α + 1/2 · g · t² (y0 = 0)
0 = 300 feet/(t · cos 45°) · t · sin 45° - 1/2 · 9.8 m/s² · t²
0 = 300 feet · sin 45°/cos45° - 4.9 m/s² · t² (sin45°/cos45° = 1)
0 = 300 feet - 4.9 m/s² · t²
-300 feet = -4.9 m/s² · t²
-300 feet / -16.08 ft/s² = t²
t = 4.32 s
Now, we can calculate the initial velocity:
300 feet /( t · cos 45°) = v0
300 feet /( 4.32 s · cos 45°) = v0
v0 = 98.22 ft/s
The initial speed of the ball is 98.22 ft/s
To obtain the maximum height of the ball, we have to find at which time the ball is at its maximum height. We can do this in several ways, but we will use the equation of velocity. See in the figure that when the ball is at its maximum height, the y-component of the velocity is zero (because the vector is horizontal). Then, using the equation of the y-component of the velocity:
vy = v0 · sin α + g · t
0 = 98.22 · sin 45° - 32.15 ft/s² · t
(-98.22 · sin 45°) / - 32.15 ft/s² = t
t = 2.16 s
(Notice that this time is half the total time of flight calculated above (4.32 s). This is also the time at which the horizontal distance traveled by the ball is half the total horizontal traveled distance. This is so because the trajectory of the ball is a parabola).
Now that we have the time, we can calculate the y-component of the position vector (r1y in the figure).
r1y = v0 · t · sin α + 1/2 · g · t²
r1y = 98.22 ft/s · 2.16 s · sin 45° - 1/2 · 32.15 ft/s² · (2.16 s)²
r1y = 75.02 ft
The maximum height of the ball is 75.02 ft.
Which number is 10 times the value of the 4 in 283.47 ?
Answer:
No answer sorry.
Step-by-step explanation:
10 times 4 ten thousands = 40 ten thousands = 4 hundred thousands. Explain how you know this equation is true. 10 × 4 ten thousands = 40 ten thousands = 4 hundred thousands.
Answer:
Value of 4= 0.4
10 x 0.4 = 4
Step-by-step explanation:
Factor.
3x(y−4)−2(y−4)
Enter your answer in the box.
Answer: Use the distributive property to multiply 3 by y−4.
3y−12−2(y−4)
Use the distributive property to multiply −2 by y−4.
3y−12−2y+8
Combine 3y and −2y to get y.
y−12+8
Add −12 and 8 to get −4.
Anwser:
y−4
Step-by-step explanation:
Hope this helps!
What is the missing term in the factorization?
100x2−36=4(5x+?)(5x−3)
Enter your answer in the box.
Answer:
100x^2-36=4(5x+3)(5x-3)
[tex]x^{2} +2x-24[/tex]
Solve for x. −23(3x−4)+3x=56
A. x=−196
B. x=−116
C. x=216
D. x=296
Answer:
x = 6/11
Step-by-step explanation:
−23(3x−4)+3x=56
Distribute
-69x + 92 +3x = 56
Combine like terms
-66x+92 = 56
Subtract 92 from each side
-66x+92-92 = 56-92
-66x =-36
Divide each side by -66
-66x/-66 = -36/-66
x = 6/11
Answer:
x=6/11
Step-by-step explanation:
Un conjunto de 10 000 observaciones tiene una distribución normal con media de
450. Si 1700 de ellas están comprendidas entre 450 y 460. ¿Cuál es la desviación
estándar?
Answer:
567898765
Step-by-step explanation:
2x - 6 >8
What is the Second Step?
Answer:
8
Step-by-step explanation:
i used the calculator
1.Add 66 to both sides.
[tex]2x=8+6[/tex]
2. Simplify 8+6 to 14
[tex]2x=14[/tex]
3. Divide both sides by 22.
[tex]x=14/2[/tex]
4. Simplify [tex]14/2[/tex] to [tex]7[/tex]
Then your answer should be [tex]x=7[/tex]
How do you determine the number of electrons? (need the answer asap)
Question 1 options:
It is equal to the atomic mass
It is equal to the protons + the atomic number
It is the atomic mass + the atomic number
It is equal to the protons in a neutral atom
Answer:
It is equal to the protons in a neutral atom
more over
#proton =#electrons=atomic number
Answer:
It is equal to the protons in a neutral atom
what is the x and y intercept of 18x-3y=15
Answer:
18(0) -3y = 15
-3y=15
now divide-3 from both sides
y= 15/-3
reduced is -5
y int = (0,-5)
18x-3(0)=15
18x=15
divide the 18 from both sides
x=15/18
reduced is 5/6
x int = 5/6
What is square 68 in simplest form
Answer:
4624 hope this helps
[tex] \sqrt{2 ^{2} } \times \sqrt{17} [/tex]
4. Simplify the radical expression and get
[tex]2 \sqrt{17} [/tex]
What is the first whole number greater than 11?
Answer:
4
Step-by-step explanation:
The √11 is ≈ 3.3166....
So the first whole number GREATER than 3.3166 is 4
-Chetan K
Answer:
√11 = 3.3166
The first whole number greater than 3.3166 is 4
Hope This Helps!
hi I was just a little bit of time with my module and I didn't know what is answer of the module now please please be sure of the answer please I want to know the answer please can I
1. 5 x 4 = A. 20
2.
[tex] \frac{2}{5} \times 25 = 2 \times 5 = 10[/tex]
the answer is D. 25
3.
[tex] \frac{3}{5} \div 15 = \frac{3}{5} \times \frac{1}{15} = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} [/tex]
the answer is A. 1/25
4.
[tex]4 \div \frac{1}{2} = 4 \times \frac{2}{1} = 8[/tex]
the answer is C. 8
5.
[tex]9 \div \frac{1}{3} = 9 \times \frac{3}{1} = 27[/tex]
the answer is D. 27
6.
[tex]20 \div \frac{1}{4} = 20 \times \frac{4}{1} = 80[/tex]
the answer is D. 80
7.
[tex] \frac{9}{10} \div \frac{1}{2} = \frac{9}{10} \times \frac{2}{1} = \frac{18}{10} = \frac{9}{5} = 1 \frac{4}{5} [/tex]
the answer is C. 1 4/5
8.
[tex]9 \div \frac{3}{2} = 9 \times \frac{2}{3} = \frac{18}{ 3} = 6[/tex]
the answer is B. 6
9.
[tex] \frac{3}{4} \div \frac{3}{8} = \frac{3}{4} \times \frac{8}{3} = 2[/tex]
the answer is A. 2
Ms. Reynold's sprinkler system has 4 stations that water all parts of her front and back lawn. Each station
runs for an equal amount of time. If it takes 36 minutes for the first 3 stations to water, how long does it
take to water all parts of her lawn?
It will take 46
minutes for Ms. Reynold to water her lawn.
Answer:
It will take 48 minutes to water all parts of her lawn.
Step-by-step explanation:
Each section runs for an equal amount of time
3 sections have run for 36 minutes
36 divided by 3 is 12, meaning each section runs for 12 minutes
12 times 4 is 48
Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial investment of P dollars in t years at an annual
interest rate of r is given by A = Pelt. Using this equation, find the value in 5 years of an investment of $2000 that earns 7% annual interest. (Round your answer to the nearest cent.)
Answer:
In this case, the equation that models the value of an initial investment of P dollars in t years at an annual interest rate of r is given by A = Pert.
Step-by-step explanation:
the area of the floor in George Square bedroom is 25 feet squared what is the length of his bedroom?
If the height of his room is 6 feet how much wall surface does he have in his room?
Answer:
1. 6.25 square feet
2. 37.5 square feet
Step-by-step explanation:
25 divided by 4=6.25
6.25x6=37.5
Answer:
Length of his bedroom is 5 Ft
Wall Surface he have in his room is 120 ft^2
Step-by-step explanation:
Please help Giving 15 points
Answer:
you said you're giving 15 points but its 8
solve pls brainliest
Answer: A= 304 feet B=1460
Step-by-step explanation:
Exits on an interstate are numbered consecutively.
The distance between Exit 5 and Exit 6 is 3.2 miles.
The distance between Exit 6 and Exit 7 is 1.1 miles farther than the distance between Exit 5 and Exit
6.
The distance between Exit 6 and Exit 8 is 2.4 miles farther than the distance between Exit 5 and Exit
7.
The distance between Exit 7 and Exit 8 is
miles.
9514 1404 393
Answer:
5.6 miles
Step-by-step explanation:
Let the following distances between exits be defined:
a = exit 5 to 6
b = exit 6 to 7
c = exit 7 to 8
Then the given relations are ...
a = 3.2
b = 1.1 +a = 4.3
(b +c) = 2.4 +(a +b) ⇒ c = a +2.4 = 5.6
The distance between exits 7 and 8 is 5.6 miles.
Help me with this please
Answer:
178 maybe tell its right or wronv
Dakota worked 55 hours over the last two weeks and his paycheck was $572.00. how much does he earn per hour
Answer:
572/55 = $10.4
or
(572 * 2)/ 55 = $20.8
Step-by-step explanation:
You divide the amount earned over the number of hours worked.
Or
if the paycheck is given monthly, the second option fits. Because $572 is half what they earned that month.
Find all triples of natural numbers (a, b, c) satisfying the system of equations
9514 1404 393
Answer:
(±7, ±1, ±4)(±13, ±11, ±16)Step-by-step explanation:
Solution of the system by the usual means yields the parametric equations ...
(a², b², c²) = (41 +t, t -7, 2t)
Since we want t-7 to be a perfect square, we can let ...
t -7 = n²
t = n² +7
Then the solutions are ...
(a, b, c) = (±√(n²+48), n, ±√(2(n² +7)))
The only integer solutions are for n=±1 and n=±11. Then the 16 possible triples are ...
(±7, ±1, ±4) and (±13, ±11, ±16) . . . where the signs can have any combination
Please help meeeeeeeeeeeeee
Answer:
⅓,⁵/12,⁵/24,⁷/48You can think about them like if they are more or less than the half of the fraction
What is the slope of the linear function graphed
below?
Answer:
y=2x+2
Step-by-step explanation:
The slope of the function is going up by 2 every time.
!HELP 20 POINTS!! Which table represents exponential growth?
Answer: The second table represents exponential growth.
Step-by-step explanation:
The second tables Y values go up with the X values so it is exponentia. The first table the Y values rise and then fall with the X values so it is not exponentia. Hope this helps!
Evaluate the expression. 4^2−3⋅4+7 Enter your answer in the box.
The answer is:
11
Hopefully this is right
Answer:
11
Step-by-step explanation:
[tex]4^{2}[/tex]-3*4+7 = 16 -12+7 = 4+7 = 11
See attachment. Please give step by step solution. Thank you
Answer:
x=19
Step-by-step explanation:
cross multiply
(−3)(+5)(3+5)=(−3)(+5)⋅2−3
(−3)⋅3=(+5)⋅2
3(−3)=(+5)⋅2
=19
your test is worth 100 points and theres 44 questions how many points is each question worth
Answer: ~ 2.27 points per question
Step-by-step explanation:
Want points/question.
So, we do 100 points / 44 questions
~ 2.27 points per question
Simplify the following integer exponents:
what is the slope of the line that contains the points (7, -1) and (-2, 2) ?
A - 1/3
B 1/3
C - 3
D - 2
Step-by-step explanation:
m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
m = [tex]\frac{2-(-1)}{(-2)-7}[/tex]
m = [tex]\frac{3}{-9}[/tex]
m = [tex]-\frac{1}{3}[/tex]
Please give me a brainliest answer
[tex]10 \times 25 \times 2255 + 52211[/tex]
SolVe it. No spam.
Answer:
=615961
Step by step explanation:
(10)(25)(2255)+52211
=(250)(2255)+52211
=563750+52211
=615961
